Control aspects of quantum computing using pure and mixed states
Thomas Schulte‐Herbrüggen, Raimund Marx, Amr Fahmy, Louis H. Kauffman, Samuel J. Lomonaco, Navin Khaneja, Steffen J. Glaser · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · 2012
Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.